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3. Beam extraction
3. Extraction of particle beams
3.1 The space charge limit and Child-Langmuirs law
3.2 External and internal fields in the extractor, laminar flow and pierce angle
3.3 The beam emittance, the acceptance of the extraction system and the conservation of phase space
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The extraction of particle beams
The plasma generator and the extraction systems are defining :
• The extracted beam current• The quality of the particle beam (emittance)
Space charge forces in the extraction system and plasma properties of the source limit the beam current.
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The space charge limit and Child-Langmuir law
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The space charge limit and Child-Langmuir law
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Current limits given by the Child-Langmuir law
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protons
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The total current extractable from an ion source is given by :
•The area covered by the extraction aperture (~ d2)
•Extraction voltage (U3/2)
•Mass of particles (1/m)1/2
•Charge state ()1/2
•The distance between the electrodes (d2)
Under the assumption that the particle source is able to produce this current. For electron sources this is usually valid, for ion sources in general not !
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The Pierce method for the design of the extraction electrodes 1
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The Pierce method for the design of the extraction electrodes 2
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Individually biased electrodes to fulfil border condition
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The Pierce method for the design of the extraction electrodes 3
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The Pierce method for the design of the extraction electrodes 4
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Beam extraction, high voltage break down limit and aspect ratio
Break down law:
maximum current density for aspect ratio of :
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Phase space distribution of a particle beam
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The beam emittance, the phase space ellipse and the twist parameters
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Phase space distribution and beam emittance
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Conservation of phase space
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Drift
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Influence of emittance on focal spot size
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Ion beam extraction from a plasma
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spac
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arge
The extractable current from an ion source is limited by :
•Space charge forces in the extraction region
•Plasma density in the source
•Production speed of ions in the plasma
•Diffusion speed of ions from the plasma into the plasma sheath
Plasma sheath : While within the plasma the charges neutralize each other, the plasma itself is biased in respect to the walls to keep an equilibrium of losses between the fast electrons and slow ions. A thin boarder area (plasma sheath) separates the plasma from the outside by an electric field.
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Influence of particle density distribution at the extraction aperture on initial phase space distribution
transversal current density profile phase spaceplasma
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Plasma density distribution at extraction aperture
Experimental set up Experimental result
Extraction aperture
lens system
aquisition
analysis
window
In praxi the particle density at the extraction aperture is not homogeneous. This will lead to non linear space charge forces within the beam transport.
Redistributions of the beam particles within the beam cause growth of the effective (RMS) beam emittance.
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The temperature of the source plasma, the potential depression in the plasma sheath and wall effects (losses of particles) are influencing the
beam emittance.
The transversal (and longitudinal) energy distribution of the beam ions is
defined by the plasma temperature and the plasma potential (electric field in
the plasma sheath)
Losses of beam ions at the extraction electrode further reduces the number of ions
to be extracted.
Wall
Wall
resolution
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Real extraction systems and the determination of beam formation
radial space chargelongitudinal
edge particles
Initial angleradial lens
focus focus without space charge
For real existing ion sources usually more than two extraction electrodes (here triode) are used to maximize beam current and to influence the beam emittance.
To calculate beam formation self consistently numerical simulation codes like EGUN, IGUN, PBGUN or Cobra are used.
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Influence of beam current and aspect ration on beam emittance
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Numerical simulation of H- extraction and transport in the LEBT for SNS using PBGUN and comparison with measured data
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Numerical simulation of the extraction of a D+ beam for IFMIF using IGUNand comparison with measured data